結果

問題 No.1763 Many Balls
ユーザー PCTprobability
提出日時 2021-10-16 05:54:06
言語 PyPy3
(7.3.15)
結果
RE  
実行時間 -
コード長 6,002 bytes
コンパイル時間 350 ms
コンパイル使用メモリ 82,176 KB
実行使用メモリ 260,192 KB
最終ジャッジ日時 2025-01-03 13:02:59
合計ジャッジ時間 94,400 ms
ジャッジサーバーID
(参考情報)
judge5 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 23 RE * 40
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

class FFT():
def primitive_root_constexpr(self,m):
if m==2:return 1
if m==167772161:return 3
if m==469762049:return 3
if m==754974721:return 11
if m==998244353:return 3
divs=[0]*20
divs[0]=2
cnt=1
x=(m-1)//2
while(x%2==0):x//=2
i=3
while(i*i<=x):
if (x%i==0):
divs[cnt]=i
cnt+=1
while(x%i==0):
x//=i
i+=2
if x>1:
divs[cnt]=x
cnt+=1
g=2
while(1):
ok=True
for i in range(cnt):
if pow(g,(m-1)//divs[i],m)==1:
ok=False
break
if ok:
return g
g+=1
def bsf(self,x):
res=0
while(x%2==0):
res+=1
x//=2
return res
butterfly_first=True
butterfly_inv_first=True
sum_e=[0]*30
sum_ie=[0]*30
def __init__(self,MOD):
self.mod=MOD
self.g=self.primitive_root_constexpr(self.mod)
def butterfly(self,a):
n=len(a)
h=(n-1).bit_length()
if self.butterfly_first:
self.butterfly_first=False
es=[0]*30
ies=[0]*30
cnt2=self.bsf(self.mod-1)
e=pow(self.g,(self.mod-1)>>cnt2,self.mod)
ie=pow(e,self.mod-2,self.mod)
for i in range(cnt2,1,-1):
es[i-2]=e
ies[i-2]=ie
e=(e*e)%self.mod
ie=(ie*ie)%self.mod
now=1
for i in range(cnt2-2):
self.sum_e[i]=((es[i]*now)%self.mod)
now*=ies[i]
now%=self.mod
for ph in range(1,h+1):
w=1<<(ph-1)
p=1<<(h-ph)
now=1
for s in range(w):
offset=s<<(h-ph+1)
for i in range(p):
l=a[i+offset]
r=a[i+offset+p]*now
r%=self.mod
a[i+offset]=l+r
a[i+offset]%=self.mod
a[i+offset+p]=l-r
a[i+offset+p]%=self.mod
now*=self.sum_e[(~s & -~s).bit_length()-1]
now%=self.mod
def butterfly_inv(self,a):
n=len(a)
h=(n-1).bit_length()
if self.butterfly_inv_first:
self.butterfly_inv_first=False
es=[0]*30
ies=[0]*30
cnt2=self.bsf(self.mod-1)
e=pow(self.g,(self.mod-1)>>cnt2,self.mod)
ie=pow(e,self.mod-2,self.mod)
for i in range(cnt2,1,-1):
es[i-2]=e
ies[i-2]=ie
e=(e*e)%self.mod
ie=(ie*ie)%self.mod
now=1
for i in range(cnt2-2):
self.sum_ie[i]=((ies[i]*now)%self.mod)
now*=es[i]
now%=self.mod
for ph in range(h,0,-1):
w=1<<(ph-1)
p=1<<(h-ph)
inow=1
for s in range(w):
offset=s<<(h-ph+1)
for i in range(p):
l=a[i+offset]
r=a[i+offset+p]
a[i+offset]=l+r
a[i+offset]%=self.mod
a[i+offset+p]=(l-r)*inow
a[i+offset+p]%=self.mod
inow*=self.sum_ie[(~s & -~s).bit_length()-1]
inow%=self.mod
def convolution(self,a,b):
n=len(a);m=len(b)
if not(a) or not(b):
return []
if min(n,m)<=40:
if n<m:
n,m=m,n
a,b=b,a
res=[0]*(n+m-1)
for i in range(n):
for j in range(m):
res[i+j]+=a[i]*b[j]
res[i+j]%=self.mod
return res
z=1<<((n+m-2).bit_length())
a=a+[0]*(z-n)
b=b+[0]*(z-m)
self.butterfly(a)
self.butterfly(b)
c=[0]*z
for i in range(z):
c[i]=(a[i]*b[i])%self.mod
self.butterfly_inv(c)
iz=pow(z,self.mod-2,self.mod)
for i in range(n+m-1):
c[i]=(c[i]*iz)%self.mod
return c[:n+m-1]
def inv_gcd(a,b):
a=a%b
if a==0:
return (b,0)
s=b;t=a
m0=0;m1=1
while(t):
u=s//t
s-=t*u
m0-=m1*u
s,t=t,s
m0,m1=m1,m0
if m0<0:
m0+=b//s
return (s,m0)
def crt(r,m):
assert len(r)==len(m)
n=len(r)
r0=0;m0=1
for i in range(n):
assert 1<=m[i]
r1=r[i]%m[i]
m1=m[i]
if m0<m1:
r0,r1=r1,r0
m0,m1=m1,m0
if (m0%m1==0):
if (r0%m1!=r1):
return (0,0)
continue
g,im=inv_gcd(m0,m1)
u1=m1//g
if ((r1-r0)%g):
return (0,0)
x=(r1-r0)//g % u1*im%u1
r0+=x*m0
m0*=u1
if r0<0:
r0+=m0
return (r0,m0)
def modpow(a,b,m):
res=1
while b:
if b%2:
res*=a
res%=m
a*=a
a%=m
b//=2
return res
def convolution_mod(a,b):
mod=90001
n=len(a)
m=len(b)
for i in range(n):a[i]%=mod
for i in range(m):b[i]%=mod
mod1=167772161
mod2=469762049
ntt1=FFT(mod1)
ntt2=FFT(mod2)
x=ntt1.convolution(a,b)
y=ntt2.convolution(a,b)
ret=[0 for i in range(n)]
for i in range(n):
tmp=crt((x[i],y[i]),(mod1,mod2))
ret[i]=tmp[0]%mod
return ret
n,m=map(int,input().split())
n%=90000
dp=[0 for i in range(n+1)]
dp[0]=1
f=[0 for i in range(n+1)]
f[0]=1
for i in range(1,n+1):
f[i]=f[i-1]*modpow(i,89999,90001)
f[i]%=90001
for i in range(m):
dp2=[0 for i in range(n+1)]
k,*a=map(int,input().split())
for j in range(k):
for x in range(0,n+1,a[j]):
dp2[x]=f[x]
dp=convolution_mod(dp,dp2)
dp=convolution_mod(dp,f)
for i in range(1,n+1):
dp[n]*=i
dp[n]%=90001
print(dp[n])
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